Spatial Dimensions
Spatial dimensions are the dimensions used in many fields of mathematics. Dimensions 'Dimension 0—a mathematical point' Dimension 0 is literally a point in space. Points can be described by coordinates, (x, y), and graphed on a coordinate plane. Since a 0-dimensional object has neither length, width, nor depth, it is immeasurable. Vertices*: 20 = 1 Total Possible Lines†: (1 * 0)/2 = 0 'Dimension 1—a line' Dimension 1 is any two 0-dimensional points connected with a line, ray, or segment. A 1-dimensional object can only be measured in length. If you were a 0-dimensional object looking at a 1-dimensional line, you would see a point that appears and disappears where the line is. In other words, the line would appear in cross-sections of points. 1-dimensional lines can stretch for an eternity. Vertices: 21 = 2 Total Possible Lines: (2 * 1)/2 = 1 'Dimension 2—a flat plane' Dimension 2 is at least two 1-dimensional lines that either connect or intersect to form a plane. A plane has width and length. To a 1-dimensional line, a plane appears as both lines and points. Vertices: 22 = 4 Total Possible Lines: (4 * 3)/2 = 6 'Dimension 3—3-dimensional space' Dimension 3 is at least two planes that either connect or intersect to form 3-dimensional space. 3-dimensional space has length, width, and height. A 2-dimensional plane would see space as a cross section of definite 2-dimensional shapes. Vertices: 23 = 8 Total Possible Lines: (8 * 7)/2 = 28 'Dimension 4—4-dimensional space' 4-dimensional space is made when at least two 3-dimensional spaces converge and/or intersect. Imagining this dimension and onwards is notoriously difficult for our minds to conjure, with each new dimension becoming increasingly complex and consequentially harder to conjure. Vertices: 24 = 16 Total Possible Lines: (16 * 15)/2 = 120 'Dimensions 5 and Above—''x-dimensional space' Each dimension after dimension 4 is a more complex version of space than the previous. For example, 5-dimensional space is made by intersecting multiple 4-dimensional spaces, and 6-dimensional space is made by intersecting multiple 5-dimensional spaces, and so on and so forth. For dimension 5, Vertices: 25 = 32 Total Possible Lines: (32 * 31)/2 = 496 For dimension 6, Vertices: 26 = 64 Total Possible Lines: (64 * 63)/2 = 2,016 For dimension 7, Vertices: 27 = 128 Total Possible Lines: (128 * 127)/2 = 8,128 For dimension 8, Vertices: 28 = 256 Total Possible Lines: (256 * 255)/2 = 32,640 For dimension 9, Vertices: 29 = 512 Total Possible Lines: (512 * 511)/2 = 130,816 (For more info on these calculations, consult notes * and †.) Dimension 0.jpg|Depiction of dimension 0. Dimension 1.jpg|Depiction of dimension 1. Dimension 2.jpg|Depiction of dimension 2. Dimension 3.jpg|Depiction of dimension 3. Dimension 4.jpg|Depiction of dimension 4. Dimension 5.jpg|Depiction of dimension 5. Dimension 6.jpg|Depiction of dimension 6. Dimensions 0 thru 9 together (JEEZUM CROW).jpg|Dimensions 0 to 9 illustrated. See Also *Number Systems *Triangles *Circles Notes *You can calculate the number of vertices an ''x-dimensional cube has with 2''x''. †All the possible unique lines that can be drawn between each of the vertices. You can calculate this using \frac{(2^x)(2^x-1)}{2}\, , where x is the number of dimensions.